The man-induced cyclostationary signatures can provide a robust mechanism for the self-coordination of cognitive radio networks. However, such artificial signatures incur signaling overhead and come at the bandwidth cost. In this paper, we show intrinsic cyclostationary signatures in the Orthogonal Frequency Division Multiplexing (OFDM) system with Cyclic Delay Diversity (CDD). The standard conformable CDD technique is initially motivated by the objective for exploiting spatial diversity. Significantly, the underlying periodicity of CDD can simultaneously induce advantageous cyclostationary signatures without any signaling overhead. The lag-indices of the CDD- induced signatures are uniquely determined by the assigned amount of cyclic delay. Consequently each CDD-OFDM system can be identified by a pre-assigned cyclic delay. The signed system can be easily and robustly recognized through cyclostationary detection. Furthermore, the CDD-OFDM systems still preserve the cyclic-prefix induced cyclostationarity as primitive OFDM. By exploiting the overall cyclostationarity, we present a desirable cyclostationarity detector with asymptotical constant false alarm rate for spectrum sensing. Comprehensive simulations are also given to show the performance improvement.